Root mean square

In mathematics, root mean square (abbreviated RMS or rms) is a statistical measure of the magnitude of a varying quantity. It can be calculated for a series of discrete values or for a continuously varying function. The name comes from the fact that it is the square root of the mean of the squares of the values. It is a power mean with the power t=2.

Related Topics:
Mathematics - Statistical - Magnitude - Function - Square root - Mean - Square - Power mean

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The rms for a collection of N values {x_1,x_2,dots,x_N} is:

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:

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x_{mathrm{rms}} =

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sqrt {{1 over N} sum_{i=1}^{N} x_i^2} =

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sqrt {{x_1^2 + x_2^2 + cdots + x_N^2} over N}

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and the corresponding formula for a continuous function f(t) defined over the interval T_1 le t le T_2 is:

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:

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x_{mathrm{rms}} = sqrt {{1 over {T_2 - T_1}} {int_{T_1}^{T_2} {}^2, dt}}.

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